Details are emerging of how such as settlement would be structured, but it raises questions about whether a deal with the government is proving more difficult than originally thought. BP is considering a plan in which it would shut down its Gulf Coast Claims Facility and divert the $14 billion that remains in that fund towards a settlement, Bloomberg News reported.

The claims fund, set up in the summer of 2010 to pay claims for businesses hurt by the spill, has doled out about $6 billion so far. The government chose attorney Kenneth Feinberg to process the claims.

“One theory says that Feinberg’s never going to spend $20 billion,” said Eric Smith, a finance professor at Tulane University and associate director of the Entergy-Tulane Energy Institute, who’s been following the case.

The settlement would, essentially, move the claims facility into the court proceeding, making it the mechanism for paying private claims in the case. Ironically, some of the plaintiffs involved in the court case had either previously claims rejected by the fund or had chosen not to participate in that process.

Any such settlement, though, appears to be moving on a different track from BP’s talks with the government, which continues to wrangle with the oil company and other defendants over possible criminal charges and fines for violations of the Clean Water Act.

BP could be liable for almost $18 billion in fines if the judge overseeing the case determines the company was grossly negligent.

In recent months, it appeared that BP and the government would come to some sort of deal before the case made it to court. That thinking gained momentum as a minority party in the Macondo well, MOEX Offshore 2007 LLC, agreed to settle government claims for $90 million.

But since then, speculation has shifted, as attorneys representing private claimants — mostly business owners and survivors of the Deepwater Horizon disaster — have seemed increasingly certain that they were nearing a settlement with BP.

With so many parties involved, and so many elements to the settlement discussions, it’s possible that even if a deal is reached with one group, other aspects of the case could still go forward before U.S. District Judge Carl Barbier in New Orleans on Monday.